After soaring to $4,000 on exchange markets over the weekend, the bitcoin cryptocurrency is continuing to rise, topping a record $4,300 on Monday — nearly $1,000 above its rate one week ago, according to data from the Coinbase currency exchange.

Bitcoin settled back under the $4,300 mark after reaching a new high Monday morning, according to several exchanges that track the decentralized currency.

"The bitcoin market cap soared past $70 billion," says CryptoCoins News, adding that a "flippening" that has been anticipated for years in the cryptocurrency community had finally come to pass, as "bitcoin now has a greater total valuation than payment-processing behemoth PayPal."

A bitcoin could be bought for around $570 just 12 months ago — reflecting a rise of around 645 percent to today's exchange rate.

Reporting on the rise, the Coindesk site says the market capitalization of all cryptocurrencies reached a record $138 billion on Monday.

The steep ascent can be attributed to a number of factors, from political concerns to a recent split into two currencies — bitcoin classic and bitcoin cash. That change, which became official on Aug. 1, was made to give the currency a more robust infrastructure; it was also tied to a move to allow large trades in the currency to occur more frequently.

Formally introduced in 2009, bitcoin has steadily accumulated both users and investors. And blockchain, the technology that underlies bitcoin, has been embraced by both academics and banking giants such as Fidelity — which now lets customers track investments in cryptocurrency — and Goldman Sachs.

Other factors, such as bitcoin's role as a hedge against political uncertainty, also play a role. A finance executive tells CNBC that South Koreans have shown a "surge of interest" in the currency as the U.S. and North Korea trade threats. The network also says there's strong interest in bitcoin in Japan, with the yen accounting for 42 percent of bitcoin currency purchases.

It's been a heady summer for bitcoin holders. After the virtual currency hit a record $2,420 in May, The Economist ran a story asking, "What if the bitcoin bubble bursts?" and wondering if its rise could be compared to historic market crazes — like the one over tulips.

Noting that "Anyone clever or lucky enough to have bought $1,000 of bitcoins in July 2010, when the price stood at $0.05, would now have a stash worth $46 million," The Economist added that "Ascents this steep are rarely sustainable" — before concluding, "If there is such a thing as a healthy bubble, this is it."